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Paper Citation Record · LEDGER

Lean-certified four-point HRT results for three lattice points and one off-lattice point

As of 12 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 2 inbound Pith citation observations for arXiv:2604.21228.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2604.21228 v1

Coverage vector

measured 5 of 5 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-08T13:42:35.503447Z

measured 7 of 7 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:29:35.580669Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-11T00:43:52.269372Z

Reference resolution

5 of 5 outbound references displayed

  • verified exact0
  • verified fuzzy2
  • unresolved3
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d6110035-4576-4958-80f9-995e77ccaf0b · outbound

This paper cites an unresolved cited work.

Lean-certified four-point HRT results for three lattice points and one off-lattice point Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-05-26T12:12:17.679487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-08T13:42:35.503447Z digest=sha256:a680705ab262141c768c168480175b820927fa29f7ab52a17961e198d7d4218b

Observation fb9e5e0a-9dae-4aa3-b484-b0bf5b81012d · outbound

This paper cites Gröchenig,Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston.

Lean-certified four-point HRT results for three lattice points and one off-lattice point Gröchenig,Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T12:12:17.675996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-08T13:42:35.503447Z digest=sha256:c4bf531013a4699a804a352da2cac813a2b74581cbe672ca391a026f1c67f5d1

Observation 4fa56926-cc44-4e7f-9ecf-45b71f72272d · outbound

This paper cites an unresolved cited work.

Lean-certified four-point HRT results for three lattice points and one off-lattice point Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-05-26T12:12:17.682912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-08T13:42:35.503447Z digest=sha256:12f3eacdec4d00451e548a659ac414c263b33719f5a4c9dcf299184160ae9f51

Observation fed197b3-289a-46ba-b137-c54cb6355067 · outbound

This paper cites an unresolved cited work.

Lean-certified four-point HRT results for three lattice points and one off-lattice point Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-05-26T12:12:17.686295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-08T13:42:35.503447Z digest=sha256:3c68716851d4d67c2b718a454f2cd769d56a5972025c24455047e7bc1d1aa37d

Observation b3cc174a-f053-4aad-ba8d-747e9a8a14e2 · outbound

This paper cites Ramanathan and T.

Lean-certified four-point HRT results for three lattice points and one off-lattice point Ramanathan and T

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T12:12:17.689371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-05-08T13:42:35.503447Z digest=sha256:39e053b2faf8293f02fc3bc9a9b993e2ecaa9a442256cff730766cbf413e9be7

Pith citing papers

Observation ac3f4a21-18e8-4d30-bd19-bee17a44f01b · inbound

An intrinsically subcritical four-point counterexample cites this paper.

An intrinsically subcritical four-point counterexample Lean-certified four-point HRT results for three lattice points and one off-lattice point

Reference 15

Resolution
verified exact
local_arxiv, observed 2026-08-11T00:43:52.277521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T00:43:52.208057Z digest=sha256:a88738a9ce9dd63948cfffbc594f9c70d387851cec0cbc495bf109de409b23ad

Observation 489123ea-0c3e-485f-a65c-db4b2665059f · inbound

The Minimum Cardinality of a Dependent Finite Gabor System Is Four cites this paper.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Lean-certified four-point HRT results for three lattice points and one off-lattice point

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-12T00:29:35.580669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T00:29:35.580669Z digest=sha256:b8e2e96fb1c327f5effa44499902d9fb5fb990129cf89bf9d361243c8e6def44